1. CPM and LP Consider the following information for a project. The following shows the network diagram for the above project. 4. There are three machines (let's say M1, M2 and M3) to produce a product. Each machine produces 30%,50% and 20% of total production, respectively. The defective production rate for each machine is 5%,3% and 2%, respectively. The quality control department randomly picked one sample and found that the sample was defective. Let D= the defective product, and P(MiD)= the probability of having the defective product from machine i. a. Find P (M1|D), P(M2D), and P (M3|D). b. Based on the information all calculations above, any recommendations to reduce the defective rate